The set of perturbation equations (REF ),
(REF ) and (REF ) are gauge-ready
equations. They can be used with any appropriate gauge choice or also
be worked out in terms of gauge-invariant
quantities [1]}, [2]}. For instance, they
can be taken in the Newtonian slicing (or zero shear) gauge \(\chi =0\) ,
with the relevant metric equations becoming
\(&&\kappa = \frac{3}{2 M_{\rm Pl}^2} ( c_s^{-1} \dot{\phi } \delta \phi -\Psi _r )\,,\\&& \alpha = -\varphi \,,\\&& \dot{\varphi } = - H \varphi -\frac{1}{3} \kappa \,.\) 
